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Question Number 138570 Answers: 1 Comments: 0

∫_( (√2)) ^2 (dx/(x^2 (√((x^2 −1)^3 )))) =?

$$\underset{\:\sqrt{\mathrm{2}}} {\overset{\mathrm{2}} {\int}}\:\frac{{dx}}{{x}^{\mathrm{2}} \:\sqrt{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} }}\:=?\: \\ $$

Question Number 138569 Answers: 1 Comments: 0

Question Number 138564 Answers: 1 Comments: 0

y∙y′=0.5∙(1+y∙c_1 )^2 ∙c_2 +0.5 y=?

$${y}\centerdot{y}'=\mathrm{0}.\mathrm{5}\centerdot\left(\mathrm{1}+{y}\centerdot{c}_{\mathrm{1}} \right)^{\mathrm{2}} \centerdot{c}_{\mathrm{2}} +\mathrm{0}.\mathrm{5} \\ $$$$ \\ $$$${y}=? \\ $$

Question Number 138560 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (−1)^n (ln (n+1)−ln (n))=?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left(\mathrm{ln}\:\left({n}+\mathrm{1}\right)−\mathrm{ln}\:\left({n}\right)\right)=? \\ $$

Question Number 138554 Answers: 1 Comments: 0

Question Number 138552 Answers: 0 Comments: 0

...nice mathemayics ... 𝛗=∫_0 ^( ∞) ((sin(tan(x)))/x)dx=(π/2)(1−(1/e)) .......

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{nice}\:\:\:\:\:\:\:\:{mathemayics}\:... \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({tan}\left({x}\right)\right)}{{x}}{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\frac{\mathrm{1}}{{e}}\right) \\ $$$$\:\:....... \\ $$

Question Number 138548 Answers: 1 Comments: 0

Question Number 138546 Answers: 1 Comments: 0

Question Number 138539 Answers: 0 Comments: 0

find the intigral of complex number I_j =∫_(γj) xdz if j=1,2 and Y_1 he is a circle ∣z∣=R

$${find}\:{the}\:{intigral}\:{of}\:{complex}\:{number} \\ $$$$ \\ $$$${I}_{{j}} =\int_{\gamma{j}} {xdz}\:\:\:{if}\:{j}=\mathrm{1},\mathrm{2}\:{and}\:{Y}_{\mathrm{1}} {he}\:{is}\:{a}\:{circle} \\ $$$$ \\ $$$$\mid{z}\mid={R} \\ $$

Question Number 138536 Answers: 0 Comments: 1

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Question Number 138533 Answers: 0 Comments: 2

∫_0 ^5 (1+x)δ(x^2 −4)dx=?

$$\int_{\mathrm{0}} ^{\mathrm{5}} \left(\mathrm{1}+{x}\right)\delta\left({x}^{\mathrm{2}} −\mathrm{4}\right){dx}=? \\ $$

Question Number 138532 Answers: 2 Comments: 0

x+(√y)=7 (√x)+y=11 faind x=? and y=?

$${x}+\sqrt{{y}}=\mathrm{7} \\ $$$$\sqrt{{x}}+{y}=\mathrm{11} \\ $$$${faind}\:\:{x}=?\:\:{and}\:\:{y}=? \\ $$

Question Number 138524 Answers: 3 Comments: 0

.......advanced ... .... ... calculus..... I:=∫_((−π)/2) ^( (π/2)) sin^2 (tan(x))dx=^(???) (π/e)sinh(1)

$$\:\:\:\:\:\:\:\:\:\:\:\:\:.......{advanced}\:...\:....\:...\:{calculus}..... \\ $$$$\:\:\:\boldsymbol{\mathrm{I}}:=\int_{\frac{−\pi}{\mathrm{2}}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}} \left({tan}\left({x}\right)\right){dx}\overset{???} {=}\frac{\pi}{{e}}{sinh}\left(\mathrm{1}\right) \\ $$

Question Number 138521 Answers: 2 Comments: 0

.......Advanced ... ... ... calculus........ Ω=∫_0 ^( ∞) ((x^2 e^x )/((1+e^x )^3 )) dx =? .....∗∗∗∗∗∗∗∗.....

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.......{Advanced}\:...\:...\:...\:{calculus}........ \\ $$$$\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{\mathrm{2}} {e}^{{x}} }{\left(\mathrm{1}+{e}^{{x}} \right)^{\mathrm{3}} }\:{dx}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:.....\ast\ast\ast\ast\ast\ast\ast\ast..... \\ $$

Question Number 138519 Answers: 0 Comments: 2

Question Number 138516 Answers: 0 Comments: 0

...........calculus ... ... ... (I)......... 𝛗=∫_0 ^( ∞) ((xe^x )/((1+e^x )^3 ))dx =? =(1/2)∫_0 ^( ∞) x.d(((−1)/((1+e^x )^2 )) ) =(1/2)[((−x)/((1+e^x )))]_0 ^∞ +(1/2)∫_0 ^( ∞) (dx/((1+e^x )^2 )) =(1/2)∫_0 ^( ∞) (1/(1+e^x ))dx−(1/2)∫_0 ^( ∞) (e^x /((1+e^x )^2 ))dx =−(1/2)[ln(1+e^(−x) )]_0 ^∞ −(1/2)∫_0 ^( ∞) d(((−1)/(1+e^x ))) =(1/2)ln(2)−(1/2)[((−1)/(1+e^x ))]_0 ^∞ =−(1/2)+(1/2)ln(2) ...

Question Number 138484 Answers: 0 Comments: 2